Nguelifack Brice M, Kemajou-Brown Isabelle
Department of Mathematics, United States Naval Academy, Annapolis, MD, USA.
Department of Mathematics, Morgan State University, Baltimore, MD, USA.
J Appl Stat. 2019 Nov 27;47(10):1794-1819. doi: 10.1080/02664763.2019.1695759. eCollection 2020.
A fully nonparametric model may not perform well or when the researcher wants to use a parametric model but the functional form with respect to a subset of the regressors or the density of the errors is not known. This becomes even more challenging when the data contain gross outliers or unusual observations. However, in practice the true covariates are not known in advance, nor is the smoothness of the functional form. A robust model selection approach through which we can choose the relevant covariates components and estimate the smoothing function may represent an appealing tool to the solution. A weighted signed-rank estimation and variable selection under the adaptive lasso for semi-parametric partial additive models is considered in this paper. B-spline is used to estimate the unknown additive nonparametric function. It is shown that despite using B-spline to estimate the unknown additive nonparametric function, the proposed estimator has an oracle property. The robustness of the weighted signed-rank approach for data with heavy-tail, contaminated errors, and data containing high-leverage points are validated via finite sample simulations. A practical application to an economic study is provided using an updated Canadian household gasoline consumption data.
当研究人员想要使用参数模型，但对于部分回归变量的函数形式或误差密度未知时，完全非参数模型可能表现不佳。当数据包含严重异常值或异常观测时，这一问题会变得更具挑战性。然而，在实际中，真实的协变量事先并不知晓，函数形式的平滑性也未知。一种稳健的模型选择方法，通过它我们可以选择相关的协变量分量并估计平滑函数，可能是解决该问题的一个有吸引力的工具。本文考虑了半参数部分可加模型在自适应套索下的加权符号秩估计和变量选择。使用B样条来估计未知的可加非参数函数。结果表明，尽管使用B样条来估计未知的可加非参数函数，但所提出的估计量具有一种近似最优性质。通过有限样本模拟验证了加权符号秩方法对于具有重尾、受污染误差的数据以及包含高杠杆点的数据的稳健性。使用更新后的加拿大家庭汽油消费数据给出了一个经济研究的实际应用。
